Most geriatric dentists say it's a type of compensatory reflex. When folks lose their teeth, suddenly they can't position their upper and lower jaws properly (it feels odd enough losing just one tooth -- imagine 32). This results in a type of oral cavity neuromuscular response to achieve some form of equilibrium. In other words, after decades of having a full set of ivories, and then suddenly having none, your jaw doesn't know where to stop or position itself. All that chewing motion stuff is the mouth trying to find the "normal resting position." Unfortunately, what you often get is the all too familiar "nose touching chin" appearance.
Of course, most people who lose their teeth get dentures. While most adapt well, others find that the new choppers just don't feel right. This dental restlessness leads to "chewing the air." Some dentists say this is just an unconscious habit most folks have of moving or manipulating objects that are being held but not used, such as when you're holding coins in your hand, and you find yourself fiddling with them.
Yet another theory of why some elderly people "chew their cud" is that with no lower teeth, the tongue is no longer confined to the space within the dental arch. This results in the tongue actually increasing in size. What appears to be a chewing motion is actually a subconscious effort to find a place for the tongue. OK, everybody at once: Ewwww. *